Boehner said on Thursday that the comments – made in a letter from Bachmann to the state department and Minnesota congressman Keith Ellison – about the family of Huma Abedin were "pretty dangerous".

He joins John McCain in rebuking Bachmann over claims that Abedin's father, mother and brother were connected to the Islamist group.

In her letter, Bachmann questioned how, given her 'family connections', Abedin had been given security clearance. Bachmann, citing foreign news reports, suggested that Abedin's relatives were known to be connected to Muslim Brotherhood operatives or organisations.

This was especially worrying as Abedin's position "affords her routine access to the secretary and policy-making", Bachmann added.

In the letter, Bachmann wondered how Abedin was not disqualified for a US security clearance "given what we know from the international media about Abedin's documented family connections with the extremist Muslim Brotherhood."

Speaking on Thursday, Boehner said: "From everything I do know of [Abedin], she has a sterling character, and I think accusations like this being thrown around are pretty dangerous". He added that he did not know Abedin personally.

Boehner became the second senior party member in as many days to publicly rebuke Bachmann over the comments. On Wednesday, McCain took to the Senate floor to defend Abedin. Without mentioning Bachmann by name, McCain described the attacks on Abedin, a Muslim, as an example of ignorance and fear.

"Huma represents what is best about America – the daughter of immigrants, who has risen to the highest levels of our government on the basis of her substantial personal merit and her abiding commitment to the American ideals that she embodies so fully.

"I am proud to know Huma and to call her my friend," McCain added.

McCain, who ran against Barack Obama for the White House in 2008, pointed out that Abedin's father died two decades ago, and that Bachmann failed to provide "one instance of an action, decision or a public position that Huma has taken while at the state department that would lend credence to the charge that she is promoting anti-American activities within our government".

McCain added: "When anyone, not least a member of Congress, launches specious and degrading attacks against fellow Americans on the basis of nothing more than fear of who they are and ignorance of what they stand for, it defames the spirit of our nation, and we all grow poorer because of it."

The furore around Bachmann's comments come a week after Clinton, the secretary of state, became the most senior member of the US government to meet with new Egyptian president Mohamed Morsi, the Muslim Brotherhood leader.

The White House is attempting to cultivate new ties with Egypt's new Islamist rulers following the removal of the Hosni Mubarak, the hardline president who was formerly backed by Washington, last year.

Abedin, the wife of former New York congressman Anthony Weiner, has been an aide to Clinton for more than 15 years, and currently serves as the state secretary's deputy chief of staff.

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